Was Plato a Pythagorean? Horky argues that he was. But, as Horky knows, the question is not simple. It turns on what one makes of the term Pythagorean and how one reads Plato. Since neither of these factors is simple or self-evident, the relation between the two is hard to determine, and any assessment of it is bound to provoke debate. I start by noting that Horky’s general case is in good order. The work itself is divided between the two factors, approached in the right order and with due scholarly caution. Chapters 1 to 3 are devoted to fleshing out what Horky calls ‘mathematical’ Pythagoreanism, while Chapters 4 to 6 cover ‘mathematical Pythagorean’ themes in Plato as found in certain passages of the Cratylus , the Phaedo and, more loosely, the Philebus and the late dialogues in Chapter 6. The study as a whole is uniformly of high quality, but the first half of the book strikes me as more successful than the second.

Since the history of Pythagoreanism is liable to be an obscure topic even to those who have an interest in ancient philosophy, I start with a brief survey of the terrain, the better to situate Horky’s claims.1

Pythagoras, the Pythagoreans and Plato

That Plato’s philosophical influences included the Pythagoreans has never been denied, but the assessment of its importance has varied considerably. A strong prima facie case for the centrality of Pythagorean influence comes from the testimony of Aristotle in Metaphysics 1. In Chapter 5, Aristotle writes that the Pythagoreans (note the plural) thought that “number was the substance of all things.” In Chapter 6 he adds that, while Plato’s philosophy had some peculiarities of its own, “in most respect [it] follows these thinkers.” While Aristotle does not overlook Socrates’ influence, suggesting that Plato’s introduction of the Forms was prompted by Socrates’ search for universal definitions, Aristotle takes the way Plato describes particulars ‘participating’ in the Platonic Forms or Ideas, whose name they share, to have been influenced by the Pythagoreans: “As for ‘participation’ he only changed the name. For the Pythagoreans say that things exist by ‘imitation’ of numbers, and Plato says they exist by participation, changing the name.”2

Despite such unequivocal testimony, modern scholarship has not always been willing to follow Aristotle. A first worry is that Aristotle leaves the Pythagoreans in question unnamed. Secondly, the exponential growth of the Pythagoras legend in later ancient philosophy, as appropriated by Platonist and later Neoplatonist authors, who projected their own philosophical preoccupations onto Pythagoras and his early followers, makes it difficult for us to separate out genuine early Pythagorean doctrines from the mountain of accretions that gathered around them (for a short guide to the sources, see the helpful table in section 2 of Huffman’s Pythagoras article, referenced in note 1). Thus ‘Plato’s Pythagoreanism’ hit its modern low-water mark in the comment of by Paul Shorey in his Loeb edition of the Republic: “The student of Plato will do well to turn the page when he meets the name Pythagoras in a commentator.”3

Matters were not set on a new footing until the publication of Walter Burkert’s Lore and Science in Ancient Pythagoreanism (Harvard, 1972; English translation by Edwin L. Minar Jr.; German original 1962), a work of astounding learnedness and still fundamental for the field. The single most important thesis of that work is the claim that the master himself, Pythagoras of Samos (570-490 BCE), was no philosopher, even less a mathematician. Instead, the historical Pythagoras appears to have been a charismatic guru who, upon emigrating to Croton in southern Italy, founded an alternative, puritanical life-style based upon the doctrine of reincarnation. But if that is the case, how then did mathematics come into it?

Chapters 1 to 3: Mathematical Pythagoreanism

This is where we can rejoin Horky. With Pythagoras out of the way, scholarship since Burkert has concentrated on the Pythagoreans in the period between the master himself and Plato.4 The most important picture we get of the historical Pythagorean community before Plato comes to us via Iamblichus (ca. 245–325 CE), but most likely goes back to Aristotle. It describes a single community divided between two groups, the akousmatikoi and the mathēmatikoi. While both claimed descent from Pythagoras, it appears that the akousmatikoi denied the authenticity of the mathēmatikoi, while the latter recognized the first. In terms of doctrinal content, the akousmatikoi kept collections of sayings attributed to the master, akousmata, which provided guidance for a ritually pure life through bizarre taboos. The mathēmatikoi by contrast, engaged with wider early Greek traditions of science and mathematics—at this stage, the term mathēma is not exclusive to mathematics—, including attempted proofs and demonstrations of their claims. From the acceptance of the akousmatikoi by the mathēmatikoi, it is usually inferred that the former represent the oldest tradition, while the mathēmatikoi must have been the innovators, even though they as well must have claimed continuity with the Master. Thus, if Pythagoras himself was not a mathematician, this is where science and mathematics entered the tradition. If we attempt to refine the picture beyond that, three ‘mathematical Pythagoreans’ can be glimpsed at through the pre-Platonic mists: Archtyas of Tarentum (435/410 to 360 B.C.), preceded by Philolaus of Croton (c. 470-400 B.C.) and earliest and most misty of all, Hippasus of Metapontum (floruit c. 450 B.C.?).

In Chapter 1 (pp. 3-35), Horky lays the foundation for his approach, using Aristotle as a source and defends a strong identity between what Aristotle sometimes calls the ‘so-called Pythagoreans’ and the mathēmatikoi. For Horky they are one and the same (p. 18). A less restricted alternative could allow it to include the first-generation Academics, Aristotle’s peers, many of whom merely styled themselves Pythagoreans.

Chapter 2 (pp. 36-84) is centred on Hippasus, but starts with a broader strand, the preoccupations or pragmateia of the ‘mathematical’ Pythagoreans with ‘the honourable’ and in particular with rankings of things according to that criterion, with gods and numbers high on the list. The evidence Horky collects is enough to convince, but I note one missed opportunity: the importance of that motif earlier still in Empedocles. At 35 B17.28 Diels-Kranz, the four elements earth, fire water and air each ‘guard their honour (timē), while Empedocles consistently describes the gods as ‘mightiest in honours’: καίτεθεοὶδολιχαίωνεςτιμῆισιφέριστοι (“and long-lived gods mightiest in honours”; B21.12, 23.8 and elsewhere). Horky thereafter focuses on the evidence for Hippasus himself. Aristotle, Theophrastus, and doxographical sources attribute to him more standard cosmological lore, but also suggest that he was the initiator of the schism, that is, the founder of ‘mathematical’ Pythagoreanism. Following that, Horky considers material from Iamblichus (= 18 F11 DK) that attributes to Hippasus the notion that “Soul-number is the first paradigm of the making of the world.” Horky does not retain it as fully genuine but he thinks it goes back to the Early Academy (p. 75), and as such attests an interest in Hippasus at that period.

Chapter 3 (pp. 85-124) shifts from doctrinal matters to an investigation of the political history of the Pythagoreans in Southern Italy. From the time of the victory of Croton over neighbouring Sybaris in 510 B.C., the city of Croton, under the leadership of a Pythagoras-led community, seems to have been in a dominant position in the region, and Pythagorean ‘membership’ seems also to have been extended to the leaders in the neighbouring states. This influence came to an abrupt end around 450 B.C., but the sources on this ‘revolution’ are as sparse as they are contradictory and partisan. Horky approaches the question via the perception of Pythagoras in fourth-century Athenian sources and the fragments of Timaeus of Tauromenium (ca. 350-260 B.C.). He argues that the evidence from Timaeus provides a complementary, internal narrative in which the mathēmatikoi act as democratizing reformers against aristocratic or oligarchic akousmatikoi. This same version seems to track tales of bans directed at Pythagoreans ‘exoterics’ who published their work and thereby divulged the brethren’s secrets. Such tales circulated about Empedocles, Hippasus, Epicharmus of Syracuse, Archytas of Tarentum and Plato, among others. Timaeus’ account, Horky argues, has additional clout because it claimed to be based on inspection of documentary evidence from the different states.

Chapters 4 to 6: Plato the Pythagorean

In the second half of the study the focus shifts to Plato. Despite many good insights, Horky tries to do too much and I found the discussion hard to follow. The overarching claim is that Plato’s philosophy is an heir to the tradition of ‘mathematical’ Pythagoreanism, in so far as Plato (p. 127):

“appropriates several of the methodological strategies of the mathematical Pythagoreans in order to respond to the central issues raised by their explanations of the primary acousmata involving wisdom: 1) ‘What is second-wisest? What assigned names to things’ and 2) ‘What is wisest? Number.’”

This sets a programme for the next two substantial chapters, on language and number respectively.

In Chapter 4 (pp. 125-66) Horky introduces what he calls the ‘growing argument’ that he attributes to the comic poet Epicharmus (p. 133). The authenticity of the fragment is dubious, so that Horky’s further use of it to define Epicharmus as a mathematical Pythagorean is strained. The argument poses the question of the stability and identity of material objects over time, but it is hard to see what is specifically Pythagorean about it as a problem—as opposed to some interesting possible Pythagorean answers—since it is just the familiar Presocratic (or Platonic?) tension between Heraclitean flux and Parmenidean stable Being. A review of material from Philolaus as connected to two passages from the Cratylus follows, (401b11-d7 and 431e9-432c6), the upshot being that for Plato numbers and names differ: “number is only an essential quality for numbers themselves, whereas names, which are sorts of imitations, are subject to many more predicates than number” (p.165).

Chapter 5 is even denser and seeks to show ‘mathematical’ Pythagorean precedents for Platonic metaphysics up to the Phaedo and Republic. This is where Horky engages with the Aristotelian texts mentioned above and is the crucial point of contact between Plato and his ‘mathematical’ Pythagorean predecessors. The whole issue is too complex to broach in a summary, but the key point is that Philolaus’ number theory, or more plainly, the classification of all numbers as odd or even, provides Plato with a model of essential predication (for example, that 3 is essentially or inalienably ‘odd’) that Plato then uses in the final argument for the immortality of the soul in the Phaedo.

Chapter 6 (pp. 201-64) is something of an epilogue. It is an exploration of Plato’s use of the ‘first-discoverer’ motif in the later dialogues. Plato will often invoke the first-discoverer of an art, for example writing, as an indirect means of criticising practitioners of that art. Horky argues (p. 224) that the “certain Prometheus with most brilliant fire” who bestows the “gift from the gods” at Philebus 16c5, and which consists of a method of analysis into ‘one and many’ and ‘limiters and unlimited’, is Plato’s way of referring to the main mathematical Pythagoreans, Hippasus, Philolaus and Archytas.

I have learned much form this work, but have some reservations about the second half. That Plato was influenced by the Pythagoreans seems clear. But if, as the title implies, Horky wants to claim that tradition as Plato’s main intellectual influence, I am not convinced that he can do so at the expense of Socrates, Parmenides, Anaxagoras and the Sophists. Lastly, for an account of Pythagoreanism’s influence on Plato, I was surprised how little was made of the soul and reincarnation. Surely the Pythagoreans’ answer to the identity puzzle of the ‘growing argument’ is to distinguish the reincarnated soul or person from the mortal body as the true bearer of identity over time.

Notes:

1. For a more detailed introduction, I refer readers to the Pythagoras article in the Stanford Encyclopedia of Philosophy by Carl Huffman. 2. 987b10-13: τὴνδὲμέθεξιντοὔνομαμόνονμετέβαλεν·οἱμὲνγὰρΠυθαγόρειοιμιμήσειτὰὄνταφασὶνεἶναιτῶνἀριθμῶν,Πλάτωνδὲμεθέξει,τοὔνομαμεταβαλών.3. Republic vol. 2, 189 note f. (1st ed. 1930), quoted by C. Huffman in the preface to his Philolaus of Croton: Pythagorean and Presocratic (Cambridge, 1993). 4. The last two decades have seen a burst of activity on Pythagoreanism. To mention a few main works in chronological order: Huffman 1993 (as cited in n. 3 above); C. H. Kahn, Pythagoras and the Pythagoreans. A Brief History (Indianapolis, 2001); C. Riedweg, Pythagoras: His Life, Teaching and Influence transl. by S. Rendall (Ithaca, 2005); C. Huffman, Archytas of Tarentum (Cambridge, 2005); L. Zhmud, Pythagoras and the Early Pythagoreans, transl. K. Windle and R. Ireland (Oxford, 2012); M. Schofield, ed. Aristotle, Plato and Pythagoreanism in the First Century B.C. (Cambridge, 2013).